1. Field of the Invention
The present invention relates to a track control method for a robot, and more particularly, to a track control method for a robot, in which a workpiece can be moved along a predetermined track with respect to a fixed point of operation so that a required operation can be accomplished.
2. Description of the Related Art
Conventionally, in an articulated playback robot, for example, and end effector, e.g., a welding torch, which is mounted on an end effector mounting portion at the distal end of a series of arms supported by means of the body of the robot, is moved for a welding operation along a predetermined track with respect to a workpiece kept at a standstill. FIG. 2 is a schematic view of the robot of this type, in which reference symbols X, Y and Z represent a three-dimensional rectangular reference coordinate system (body coordinate system) whose origin lies on one point O on the robot body. In this reference coordinate system, the workpiece is kept in a stationary state. Symbol U designates the coordinate position, in the reference coordinate system, of the origin of a workpiece coordinate system set for the workpiece.
Prior to the execution of actual operation by means of the robot, the robot is previously instructed of, for example, two target points on the track of the end effector. Symbols P1 and P2 indicate the coordinate positions of first and second target points, respectively, in the workpiece coordinate system.
First, an operator operates the various arms so that the operating position (point of operation) of the end effector, e.g., the position of the tip end of the welding torch, is coincident with the first target point P1. By this operation, the end effector mounting portion at the distal end of the arms is caused to take a coordinate position R1 in the reference coordinate system. Then, the operator instructs the robot of the target point P1. In response to this teaching operation, the operating states (operating positions of individual axes) of various robot operating sections, including joints between the arms of the robot, at the target point P1, are detected by means of various sensors attached to the robot, and these detected operating states are stored as control information.
Subsequently, the arms are operated so that the point of operation of the end effector is coincident with the second target point P2, with a coordinate position T of the point of operation of the end effector, in an end effector coordinate system (mechanical interface coordinate system) set for the end effector mounting portion, kept fixed. As a result, the end effector mounting portion takes a coordinate position R2 in the reference coordinate system. At the target point P2, the same teaching operation as aforesaid is performed, and the operating positions of the individual axes at this point of time are stored.
In the actual operation, the robot performs the required operation in a manner such that the point of operation is moved along the predetermined track.
Here let us consider the coordinate position of the point of operation in the reference coordinate system. In general, the sensors serve to detect the operating states of their associated robot operating sections, in a coordinate system set for the operating sections. In order to obtain the coordinate position of the end effector mounting portion in the reference coordinate system in response to these detected states, therefore, a series of coordinate system transformations are performed with respect to the detected parameter values. The coordinate position of the end effector mounting portion after this series of coordinate system transformations will hereinafter be designated by [R]. In order to obtain the coordinate position of the point of operation of the end effector in the reference coordinate system, moreover, coordinate system transformation for the end effector, from the end effector coordinate system to the reference coordinate system, that is, coordinate system transformation corresponding to the posture of the end effector relative to the end effector mounting portion, is performed. A coordinate system transformation matrix for this transformation will hereinafter be designated by [T].
Since values in the workpiece coordinate system are given individually to the target points P1 and P2, on the other hand, coordinate system transformation is performed to represent these target points in terms of the reference coordinate system. Hereinafter, the coordinate position of the target point in the workpiece coordinate system will be designated by [P], and a coordinate system transformation matrix for transformation from the workpiece coordinate system to the reference coordinate system will be designated by [U].
Since the point of operation and the target point are coincident with each other, the following equation holds: EQU [R][T]=[U][P]. (1)
From equation (1), we obtain EQU [P]=[U].sup.-1 [R][T]. (2)
In the conventional robot, as described above, the position of the point of operation of the end effector relative to the end effector mounting portion is fixed, and the workpiece is fixed, so that the coordinate system transformation matrices [T] and [U] are constant. Thus, if the coordinate positions [R] of the end effector mounting portion corresponding to the coordinate positions [P] (P1 and P2) of the first and second target points, given for instruction in the aforesaid manner, are obtained, and if the coordinate position of each interpolating point between the two target points is [P], the coordinate position [R] at each interpolating point is given by EQU [R]=[U][P][T].sup.-1. (3)
At the time of playback operation, the track of the point of operation is controlled in accordance with the series of coordinate positions of the end effector mounting portion or the distal end of the arms in the reference coordinate system, obtained in the aforesaid manner.
According to the conventional method, however, it is impossible to perform an operation such that the positional relationship between the distal end of the arms and the point of operation of the end effector, that is, the transformation matrix [T], changes with the passage of time. It is impossible, for example, to perform a welding operation in which the workpiece is moved relatively to a fixed welding torch, for welding.